Question

Mrs. gomes found that 40% of students at her high school take chemistry. she randomly surveys 12 students. what is the probability that exactly 4 students have taken chemistry? round the answer to the nearest thousandth.

Answer 1

The probability that a student takes chemistry = 0.4

P = 0.4

The probability that a student does not take chemistry = 0.6

Q = 0.6

Using binomial distribution theorem we have

P(x) = ⁿCₓ Pˣ Qⁿ⁻ˣ

Here x = 4 as we need to find for exactly 4 students, and n = 12

So,

P(4) = ¹²C₄ (0.4)⁴ (0.6)⁸

= 495 (0.0256) (0.0168)

= 0.21289

P = 0.213